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n j=1 x i+j−1 , i ≥ 1, is called the Fibonacci orbit of G with respect to the generating set A, denoted F A (G). If F A (G) is periodic we call the length of the period of the sequence the Fibonacci length of G with respect to A, written LEN A (G). In this paper we examine the Fibonacci lengths of D i 2m , i > 1 where D 2m is the dihedral group of order 2m.

For a finitely generated group G = A where A = {a 1 , a 2 ,. .. , a n } the sequence x i = a i+1 , 0 ≤ i ≤ n − 1, x i+n = n j=1 x i+j−1 , i ≥ 0, is called the Fibonacci orbit of G with respect to the generating set A, denoted F A (G). If F A (G) is periodic we call the length of the period of the sequence the Fibonacci length of G with respect to A, written… (More)

For a finite group G = =X (X = G), the least positive integer ML X (G) is called the maximum length of G with respect to the generating set X if every element of G may be represented as a product of at most ML X (G) elements of X. The well-known commutator length of a group G, denoted by c(G), satisfies the inequality c(G) ≤ ML(G), where G is the derived… (More)

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